Question

In a linear pair, if one angle measures 12 degrees less than half the other angle, what are the measures of the angles?

A) 48°, 96°
B) 60°, 120°
C) 72°, 144°
D) 84°, 168°

Answer 1

In a linear pair, the sum of the measures of the angles is always 180 degrees. By setting up and solving an equation, we can find the measures of the angles.

Step-by-step explanation:

In a linear pair, the sum of the measures of the angles is always 180 degrees. Let's denote one angle as x and the other angle as 2x - 12. We can set up the equation x + (2x - 12) = 180 and solve for x.

x + 2x - 12 = 180

3x - 12 = 180

3x = 192

x = 64

Now we can substitute x into the equation to find the measures of the angles. One angle is 64 degrees and the other angle is 2(64) - 12 = 116 degrees.

Therefore, the measures of the angles are 64 degrees and 116 degrees.